Why are there square artifacts in my render?
The reason for discrepancy are different settings for preview and render of the Multires modifier.

From manual:


  Preview
      Set the level of subdivisions to show in the 3D View.  
  
  Sculpt
      Set the number of subdivisions to use in Sculpt Mode.  
  
  Render
      Set the number of subdivisions to show when rendering.


In your file, Render option is set to 1, and thus it uses the first level of subdivision when rendering image. 



On this level mesh becomes more bumpy and with rough sides, which reflect the light you see on the rendered image.
It is not visible in 3D Viewport because Preview is set to 2, which makes mesh smoother only for previewing it in the viewport.

See related answers:

Object appears smoothed after rendering but not in viewport - specific case with Multires modifier.

Cycles viewport render different than f12 render? - general things to consider when preview and render results differ.